Difference between revisions of "Silicon Slab Calculations"
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PBE diamond bulk 1102.9319 bohr^3 = 20.4971 Å<sup>3</sup> | PBE diamond bulk 1102.9319 bohr^3 = 20.4971 Å<sup>3</sup> | ||
| − | ==Annotated | + | ==Annotated Bibliography== |
| − | * | + | * [https://dx.doi.org/10.1088/1367-2630/8/9/200 Pengpeng Zhang et al 2006 New J. Phys. 8 200] <br />Page 12:"A major difference now is that the π∗ surface band introduces a high density of available electronic states in the Si bandgap, acting therefore as a sink for electrons." <br />Figure 4: "The existence of the surface bands results in a reduced effective bandgap (∼0.35eV in this example)between the bulk VBM of the SiNM and the bottom of the surface π∗ band." |
Revision as of 11:18, 26 June 2024
Contents
Energy Under Strain
PBEsol
File:Si.PBEsol.Diamond-1 ML.Strain vs Cohesive Energy.png
Phonons
| Method | Pseudopotential | Phonons | Brillouin Zone | Reference |
|---|---|---|---|---|
| DFPT-PZ a = 5.424 Å |
Norm-conserving (TM) | File:Si.001.PZ.freq.Fritsch1995.png | File:Fd-3m.001.BZ.png | Fritsch (1995) |
| DFPT-PBEsol (incorrect celldm(1)) |
Ultrasoft | File:Old.Si.1 ML.PBEsol.freq vdos.png | ||
| DFPT-PBEsol | Ultrasoft | File:Si.1 ML.PBEsol.freq vdos.png |
Tests
Vacuum
- Si.pbe-n-rrkjus_psl.1.0.0.UPF, Ecut wfc/rho = 50/500, startingwfc='atomic', celldm(1)=10.335466, kpoint: 2-2-1-1-1-0, Gamma q-point
| Celldm(3) | 1.0 | 1.2 | 1.4 | 1.6 | 1.8 | 2.0 | 2.2 | 2.4 | 2.6 | 2.8 | 3.0 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Energy (Ry) | -91.05486611 | -91.02905414 | -90.96623064 | -90.97347954 | -90.97924947 | -90.98131755 | -90.98193937 | -90.98209842 | -90.98212589 | -90.98212146 | -90.98211064 |
| Frequency (THz) | 21.399668 | 14.956531 | 14.683791 | 14.821677 | 14.864115 | 14.871671 | 14.875238 | 14.875516 | 14.874547 | 14.876260 | 14.877172 |
| Celldm(3) | 3.0 | 3.2 | 3.4 | 3.6 | 3.8 | 4.0 | 4.2 | 4.4 | 4.6 | 4.8 | 5.0 |
| Energy (Ry) | -90.98211064 | -90.98210091 | -90.98209100 | -90.98208215 | -90.98207546 | -90.98207052 | -90.98206569 | -90.98206092 | -90.98205683 | -90.98205416 | -90.98205135 |
| Frequency (THz) | 14.877172 | 14.875561 | 14.875605 | 14.884300 | 14.876991 | 14.876809 | 14.882501 | 14.878010 | 14.878940 | 14.879234 | 14.870053 |
| Structure | Pseudopotential | nq1 | nq2 | nq3 | Frequency (THz) | Time | |||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Infinite Crystal | Si.pz-n-rrkjus_psl.1.0.0.UPF | 4 | 4 | 4 | 14.686825 | 5010 min | |||||
| 1 Monolayer | * | * | * | * | * | * | |||||
| Total Energy | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| X/Y Mesh | 1 1 1 | 2 2 1 | 4 4 1 | 6 6 1 | 8 8 1 | 10 10 1 | 12 12 1 | 14 14 1 | 16 16 1 | 18 18 1 | 20 20 1 |
| PBE | NC | -91.15925071 | -90.98188148 | -90.98096535 | -90.98091576 | -90.98081652 | -90.98085760 | -90.98086999 | -90.98086058 | -90.98086731 | -90.98086589 |
| LDA/PZ | -90.82372513 | -90.65027160 | -90.64955939 | -90.64955378 | -90.64952796 | -90.64956158 | -90.64958106 | -90.64957675 | -90.64956582 | -90.64957273 | -90.64957249 |
| Total Energy (Ry) | ||||||
|---|---|---|---|---|---|---|
| x y z | * * 1 | * * 2 | * * 4 | * * 6 | * * 8 | |
| 1 1 * | NC | NC | NC | NC | NC | |
| 2 2 * | -90.48534325 | -90.48716920 | NC | -90.48717819 | -90.48717698 | |
| 4 4 * | -90.50777500 | -90.50932817 | -90.50934385 | -90.50934449 | -90.50934394 | |
| 6 6 * | -90.50934449 | NC | NC | -90.50718812 | not run | |
| 8 8 * | NC | not run | not run | not run | NC | |
Mesh Center
- Quantum ESPRESSO using PS Library 1.0 PZ RRKJ US pseudopotential with Ecut,wfc/rho = 50/500 Ry
- Relaxed atomic coordinates using PP-relaxed lattice parameter a = 10.708 Bohr and 1.6a of vacuum in a3 direction
- Smallest converged grid parameter was 2 2 2
| Mesh Center Point | Total Energy (Ry) | SCF Cycles |
|---|---|---|
| 0 0 0 | -90.48716920 | 93 |
| 1 0 0 | -90.52916013 | 61 |
| 0 0 1 | -90.48718293 | 54 |
| 1 1 0 | -90.48939869 | 38 |
| 1 1 1 | -90.48939583 | 63 |
- Add 10 10 1 at different k-point grid offsets
- At best k-point grid offset with 2 2 1 and 2 2 2 k-point grids, check total energy change for celldm(3) = 1.0, 1.2, 1.4, 1.6, 1.8, 2.0, etc. until less than 0.0001 Ry
- Then, run all x x 1 at the most stable k-point grid offset until total energy changes less than 0.0001 Ry
Structure
- DFT-PBE
1-ML
| Modification | Total Energy (Ry / 8 atoms) | Total Force (Ry / a0 / 8 atoms) | ω [Γ (1-3)] (THz) | ||
|---|---|---|---|---|---|
| Bottom of Cell | -90.9808882393 | 0.001189 | -1.707084 | -0.235194 | -0.132992 |
| Centered in Cell | -91.05494884 | 0.000220 | -0.317949 | -0.195414 | 0.172351 |
| Built-In Phonon | -91.05494922 | 0.000241 | -0.329813 | -0.229082 | 0.016019 |
| 2x2 Supercell | -91.05616393 | 0.000913 | |||
Build In Displacement Vector
Γ-point, lowest frequency mode
| Displacement Factor | Total Energy (Ry / 8 atoms) | Total Force (Ry / a0 / 8 atoms) | ω [Γ (1-3)] (THz) | ||
|---|---|---|---|---|---|
| 0.0 | -91.05490108 | 0.001967 | |||
| 0.1 | -91.054481 | 0.016412 | -0.322887 | -0.189111 | 0.340710 |
| 0.2 | -91.053070 | 0.032972 | -0.364120 | -0.221765 | 0.371472 |
| 0.3 | -91.050710 | 0.049779 | -0.308852 | -0.191316 | 0.326616 |
| 0.4 | -91.047394 | 0.066933 | -0.348059 | -0.270962 | 0.367059 |
| 0.5 | -91.043114 | 0.084544 | -0.284463 | -0.151811 | 0.320345 |
| 0.6 | -91.037859 | 0.102744 | -0.345105 | -0.153570 | 0.498687 |
| 0.7 | -91.031620 | 0.121659 | -1.000608 | -0.236214 | -0.135593 |
| 0.8 | -91.024383 | 0.141412 | -1.583491 | -0.278128 | -0.180348 |
| 0.9 | -91.016139 | 0.162127 | -2.078362 | -0.369162 | -0.281689 |
| 1.0 | -91.006881 | 0.183921 | -2.543886 | -0.341077 | -0.267751 |
2-ML
| Modification | Total Energy (Ry / 8 atoms) | Total Force (Ry / a0 / 8 atoms) | ω [Γ (1-3)] (THz) | ||
|---|---|---|---|---|---|
| Bottom of Cell | -91.118108725 | 0.000038 | -7.411048 | -3.947619 | -1.719877 |
| Centered in Cell | -91.11810858 | 0.0000405 | -0.317949 | -0.195414 | 0.172351 |
Volume
PBE diamond bulk 1102.9319 bohr^3 = 20.4971 Å3
Annotated Bibliography
- Pengpeng Zhang et al 2006 New J. Phys. 8 200
Page 12:"A major difference now is that the π∗ surface band introduces a high density of available electronic states in the Si bandgap, acting therefore as a sink for electrons."
Figure 4: "The existence of the surface bands results in a reduced effective bandgap (∼0.35eV in this example)between the bulk VBM of the SiNM and the bottom of the surface π∗ band."
